Let A and B be two events such that P(bar(A ∪ B)) = 1/6, P(A ∩ B) = 1/4 and P(bar A) = 1/4. Then the events A and B are …

Question

Let A and B be two events such that P(\(\overline{A∪B}\)) = 1/6, P(A ∩ B) = 1/4 and P(\(\bar{A}\)) = 1/4. Then the events A and B are …

(a) Equally likely but not independent 

(b) Independent but not equally likely 

(c) Independent and equally likely 

(d) Mutually inclusive and dependent

Answer 1

(b) Independent but not equally likely 

So P(A). P(B) = (3/4) x (1/3) = 1/4

P(A ∩ B) = P(A). P(B) 

⇒ A and B are independent and not equally likely